Deep neural networks are easily fooled by small perturbations known as adversarial attacks. Adversarial Training (AT) is a technique aimed at learning features robust to such attacks and is widely regarded as a very effective defense. However, the computational cost of such training can be prohibitive as the network size and input dimensions grow. Inspired by the relationship between robustness and curvature, we propose a novel regularizer which incorporates first and second order information via a quadratic approximation to the adversarial loss. The worst case quadratic loss is approximated via an iterative scheme. It is shown that using only a single iteration in our regularizer achieves stronger robustness than prior gradient and curvature regularization schemes, avoids gradient obfuscation, and, with additional iterations, achieves strong robustness with significantly lower training time than AT. Further, it retains the interesting facet of AT that networks learn features which are well-aligned with human perception. We demonstrate experimentally that our method produces higher quality human-interpretable features than other geometric regularization techniques. These robust features are then used to provide human-friendly explanations to model predictions.

提出了一种使用二次近似的拟合函数的新型规则化器，并通过迭代计算逼近最坏情况二次损失，从而在具有良好的鲁棒性的同时避免了梯度混淆和降低了训练时间。实验证明，该模型产生的人类可解释性特征优于其他几何正则化技术，并且这些鲁棒特征可用于提供人性化的模型预测解释。

对抗鲁棒性和可解释性的二阶优化